Posted by Brianna on Thursday, September 27, 2012 at 2:39pm.
Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is 86.0 mph. Bob starts the stopwatch as he throws the ball (with no way to measure the ball\'s initial trajectory), and watches carefully. The ball rises then and then falls, and after 0.910 seconds the ball is once again level with Bob. Bob can\'t see well enough to time when the ball hits the ground. Bob\'s friend then measures that the ball landed 453 ft from the base of the cliff. How high up is Bob, if the ball started from exactly 5 ft above the edge of the cliff?

Physics based Calculus  Steve, Thursday, September 27, 2012 at 4:48pm
height of ball above cliff is
h = 5 + vy*t  16t^2
assuming vy is ycomponent of maximum speed of 86 mph = 126.13 ft/s
h = 0 after .910 sec, so
vy = 9.1 ft/s
now, vy^2 + vx^2 = v^2
9.1^2 + vx^2 = 126.13^2
vx = 125.8 ft/s
ball fell from cliff height
453/125.8 = 3.6 sec
after falling back to cliff height, the distance fallen to ground was
9.1t + 16t^2 = 241 ft
so, the cliff is 241 ft high
Answer This Question
Related Questions
 Physics  Bob has just finished climbing a sheer cliff above a beach, and wants...
 College Physics  Bob has just finished climbing a sheer cliff above a beach, ...
 Calculus/Physics  A stone is thrown from a cliff top with an upward velocity of...
 physics  A projectile is launched straight up at 55.5 m/s from a height of 73.5...
 physics  A student stands at the edge of a cliff and throws a stone ...
 Language Arts  1. Which of the following transitions shows a comparison? A. ...
 Physics  Hey, I'm studying for my physics class, and I'm not sure how to solve ...
 Physics  You are driving off of a horizontal cliff, and your car has a ...
 Physics  You are driving off of a horizontal cliff, again!!! The cliff is ...
 physics  A student stands at the edge of a cliff and throws a stone ...
More Related Questions